In [1]}, we proposed a low rank tensor VP solver to dynamically and adaptively build up low rank solution basis based on
the observation that the differential operator in the Vlasov equation can be represented in a tensorized form. In particular, we start from a low rank solution in a tensor format and add additional basis by applying the well-established high order finite difference upwind method coupled with the strong-stability-preserving (SSP) multi-step time discretizations [2]}; the solutions are being further updated by an SVD-type truncation to remove redundant bases. We further generalize the algorithm to high-dimensional problems with the HT decomposition, which attains a storage complexity that is linearly scaled with the dimension, mitigating the curse of dimensionality.
